Cylindrical Indenter Research Articles

Behind Amor Blunt Trauma Lung and Liver Strains from Indenter Loading via Finite Element Modeling

Abstract To determine behind armor blunt trauma injury criteria, experiments have been conducted to launch projectiles at live swine at velocities ranging up to 65 m/s using one type of indenter design. To ensure the generalizability of the developed injury criteria, tests are needed with other indenter designs. The objectives of this study were to evaluate the kinematics and injury parameters from two indenter designs using human body finite element modeling. The simulation matrix consisted of indenter designs of chord and cylindrical shape, and 150 and 230 grams (g) mass, with impacts to liver and lung regions at 30 and 60 m/s. Rib and lung strains from lung impacts, and rib strains and liver strain energy densities from liver impacts were used to evaluate the design variables of mass and shape. Both designs played a role in skeletal and organ injury parameters. Analysis revealed the increased susceptibility for skeletal and organ traumas with the high mass indenter at high velocity impacts. The cylindrical indenter may be protective for organ injuries due to the larger area of loading on the ribcage compared to the chord indenter. Results from the chord indenter may serve as a conservative estimate of injury criteria.

Measurement of fracture toughness in high-strength alloys via modified limit load analysis using flat-end cylindrical indenter

Measurement of fracture toughness in high-strength alloys via modified limit load analysis using flat-end cylindrical indenter

Experimental analysis of quasi‐static indentation in composite sandwich multilayers with corrugated core

AbstractThis study examines the effects of multilayering in sandwich panel composite structures with different corrugated core configurations under quasi‐static indentation loading. The panels were fabricated using woven glass fibers and epoxy resin via the Vacuum Infusion Process. Experiments were conducted using two hemispherical cylindrical indenters with a diameter of 20 mm (ID = 20 mm) and 10 mm (ID = 10 mm) and the behavior of the composite structure in terms of contact force and fracture mechanisms for different core corrugations (square and butterfly) were investigated in two ways with foam and without foam. The experimental results demonstrate that, among corrugated core geometries without foam, butterfly cores outperform square cores in terms of structural strength, maximum force, moment force, energy absorption, specific energy absorption, and displacement until full indentation. Moreover, the butterfly core shows a higher peak load and different failure mechanisms compared to the square core. Under loading with a 10 mm indenter, the butterfly core without foam only experienced perforation in the loading area, without fracture completely. Also, adding foam did not change failure mechanisms and mechanical behavior in the butterfly geometry. However, in the square geometry, foam filled gaps between the core, preventing fracture completely and leading to only perforation in the loading area, unlike the specimen without foam. The visual analysis during the quasi‐static indentation process revealed several significant damage mechanisms, including matrix cracking, fiber breakage, delamination, buckling and crushing of cell walls, damage to top sheets, core separation, and complete indentation of the samples.Highlights Delamination and indentation failure mechanisms were seen on the butterfly core. Skin indentation and rib fracture failure mechanisms were seen on the square core. Butterfly corrugated cores revealed the best performance without/with foam. The core shape was more effective on the strength than the foam addition.

Deep Indentation Tests of Soft Materials Using Mobile and Stationary Devices.

Measurements of the properties of soft materials are important from the point of view of medical diagnostics of soft tissues as well as testing the quality of food products and many technical materials. One of the frequently used techniques for testing such materials, attractive due to its non-invasive nature, is the indentation technique, which does not puncture the material. The difficulty of testing soft materials, which affects the objectivity of the results, is related to the problems of stable positioning of the studied material in relation to the indentation apparatus, especially with a device held by the operator. This work concerns the comparison of test results using an indentation apparatus mounted on mobile and stationary handles. The tested materials are cylindrical samples of polyurethane foams with three different stiffnesses and the same samples with a 0.5 or 1 mm thick silicone layer. The study presented uses an apparatus with a flat cylindrical indenter, with a surface area of 1 cm2, pressed to a depth of 10 mm (so-called deep tests). Based on the recorded force changes over time, five descriptors of the indentation test were determined and compared for both types of handles. The tests performed showed that the elastic properties of foam materials alone and with a silicone layer can be effectively characterized by the maximum forces during recessing and retraction and the slopes of the recessing and retraction curves. In the case of two-layer materials, these descriptors reflect both the characteristics of the foams and the silicone layer. The results show that the above property of the deep indentation method distinguishes it from the shallow indentation method. The repeatability of the tests performed in the mobile and stationary holders were determined to be comparable.

Development of a recommended practice for evaluating rumble strip noise and vibration performance

As part of the NCHRP 15-68 project "Effective Low-Noise Rumble Strips" project, a recommended measurement program was developed for evaluating the noise and vibration performance of rumble strip designs. Two rumble strip designs located in Northern California, which included cylindrical indentations ground into the pavement at regular intervals and a continuous sinusoidal profile, were used to assess the input to a vehicle operator and the resultant exterior noise when the vehicle departed from the travel lane. Measurements were conducted on and off shoulder rumble strips at 60 and 45 mph with eight light vehicles ranging from small compact passenger cars to large sport utility vehicles. Six triaxial vibration measurements and six microphone locations were evaluated on the interior of the vehicle, and from these measurements, one primary and one (optional) secondary location for noise and vibration were selected for the recommended procedure. Vehicle pass-by measurements were also made following the procedures of AASHTO TP 98 Statistical Isolated Pass-By Method. While not required, on-board sound intensity (OBSI) testing is recommended to establish the off-strips pavement level. The recommended procedure is intended to be used by transportation agencies and other practitioners to assure comparable results when evaluating existing and alternative rumble strip designs.

Finite Element Analysis of the Mechanical Response for Cylindrical Lithium-Ion Batteries with the Double-Layer Windings

The plastic properties for the jellyroll of lithium-ion batteries showed different behavior in tension and compression, showing the yield strength in compression being several times higher than in tension. The crushable foam models were widely used to predict the mechanical responses to compressive loadings. However, since the compressive characteristic is dominant in this model, it is difficult to identify distributions of the yield strength in tension. In this study, a simplified jellyroll model consisting of double-layer windings was devised to reflect different plastic characteristics of a jellyroll, and the proposed model was applied to an 18650 cylindrical battery under compressive loading conditions. One winding adopted the crushable foam model for representing the compressive plastic behavior, and the other winding adopted the elastoplastic models for tracking the tensile plastic behavior. The material parameters in the crushable foam model were calibrated by comparing the simulated force–displacement curve with the experimental one for the case where the cell was crushed between two plates when the punch was displaced by 7 mm. A specific cut-off value (10 MPa) was assigned to a yield stress limit in the elastoplastic model. Further, the computational model was validated with two more loading cases, a cylindrical rod indentation and a spherical punch indentation, as the punch was displaced by 6.3 mm and 6.5 mm, respectively. For three loading cases, deformed configurations and plastic strain distributions were investigated by finite element analysis. It was found that the proposed model clearly provides the plastic behavior both in compression and tension. For the crush simulation, the maximum compressive stress approached 222 MPa in the middle of the jellyroll, and the maximum effective plastic strain approached 60% in the middle of the layered roll. For indentation with the cylindrical and the spherical punch, the maximum effective plastic strain approached 52% and 277% in the layered roll, respectively. The local crack or location of a short circuit could be predicted from the maximum effective plastic strain.

Indentation of circular hyperelastic membrane with hole by cylindrical indenter

We consider the problem of indentation of a thin circular elastic plate with a hole in the centre by a cylindrical indenter under large strains. We use the nonlinear theory of isotropic incompressible hyperelastic membranes and consider a quasi-static process of indentation. We use Coulomb’s law to describe the friction at a contact. The goals of this study are to determine and to compare the effects of friction, material parameters and pre-stretch of the membrane on the indentation process.

Study on methods measuring mechanical properties of arterial wall by macroscopic indentation

Accurately evaluating the local biomechanics of arterial wall is crucial for diagnosing and treating arterial diseases. Indentation measurement can be used to evaluate the local mechanical properties of the artery. However, the effects of the indenter's geometric structure and the analysis theory on measurement results remain uncertain. In this paper, four kinds of indenters were used to measure the pulmonary aorta, the proximal thoracic aorta and the distal thoracic aorta in pigs, and the arterial elastic modulus was calculated by Sneddon and Sirghi theory to explore the influence of the indenter geometry and analysis theory on the measured elastic modulus. The results showed that the arterial elastic modulus measured by cylindrical indenter was lower than that measured by spherical indenter. In addition, compared with the calculated results of Sirghi theory, the Sneddon theory, which does not take adhesion forces in account, resulted in slightly larger elastic modulus values. In conclusion, this study provides parametric support for effective measurement of arterial local mechanical properties by millimeter indentation technique.

On the depth of cylindrical indentation of an elastic half-space for different types of displacement boundary conditions

Nonlinear relationships between the penetration depth δ and applied force F for cylindrical indentation of a half-space are derived corresponding to two types of displacement boundary conditions: (i) zero vertical displacement imposed at points x=±b of the free-surface of a half-space, and (ii) zero vertical displacement imposed at a point z=h below the indenter. The requirement that the work done by the indentation force must be equal to the work done by the contact pressure defines the minimum values of b and h for which the indentation is geometrically and physically possible. The minimum value of b is found to be about 10 times greater than the semi-width of the contact zone a=(4FR/πE∗)1/2, with the corresponding minimum value of the indentation depth δmin≈3.5δ0, where δ0=2F/πE∗ is the height of the contact zone under applied force F, and E∗=E/(1−ν2) is the plane strain elastic modulus. The minimum value of h is equal to about 21a in the case ν=1/3, and about 27a in the case ν=1/2. The relationship between h and b, corresponding to the same indentation depth δ≥δmin, is derived and shown to be nearly linear for large values of h/a and b/a. The obtained results are used to estimate the indentation depth of finite-size elastic bodies under different boundary constraints. Comparison with FEM prediction is made.

Novel method for measuring surface residual stress using flat-ended cylindrical indentation

Instrumented indentation is a promising technique for estimating surface residual stresses and mechanical properties in engineering components. The relative difference between the indentation loads for unstressed and stressed specimens was selected as the key parameter for measuring surface residual stresses in flat-ended cylindrical indentations. Based on the equivalent material method and finite element simulations, a dimensionless mapping model with six constants was established between the relative load difference, constitutive model parameters, and normalized residual stress. A novel method for measuring the surface residual stress and constitutive model parameters of metallic material through flat-ended cylindrical indentations was proposed using this model and a mechanical properties determination method. Numerical simulations were conducted using numerous elastoplastic materials with different residual stresses to verify the proposed model; good agreements were observed between the predicted residual stresses and those previously applied in finite element analysis. Flat-ended cylindrical indentation tests were performed on four metallic materials using cruciform specimens subjected to various equibiaxial stresses. The results exhibited good conformance between the stress–strain curves obtained using the proposed method and those from traditional tensile tests, and the absolute differences between the predicted residual stresses and applied stresses were within 40 MPa in most cases.

Numerical analysis of the indentation of a poro-elastoplastic half space by a rigid cylinder

Poro-elasto-plastic cylindrical indentation as a means for material characterization is explored numerically in this work. When a rigid cylinder is being pressed into a semi-infinite, fully saturated poroelastic medium via step displacement loading, undrained and drained elastic constants are reflected in the responses at the early and late times, while hydraulic diffusivity is manifested in the transient behavior. Such an indentation test can therefore be used in principle to identify material parameters. For geomaterials, plastic deformation may occur due to the indentation action. How the hydromechanically coupled indentation response is affected by plastic deformation is investigated here using finite element analysis. We consider the problem to be plane strain with frictionless contact. Drucker-Prager failure criteria with and without a cap are considered. We show that if there is only limited plastic deformation, the concept of using the transient response for determining hydraulic diffusivity may be extended from poroelasticity to poro-elasto-plasticity.

Limit State of Bake Hardened Stamped Interstitial-free Steel Automotive Parts Caused by Local Thickness Reduction

Current trends in the complex shapes of modern automobiles lead to the need for extremely formable materials for deep drawing applications. In general Interstitial–Free (IF) steels present the solution for this purpose. In addition, the cold stamping process is influenced by a variety of input factors that must be correctly adjusted. An imperfection in one of the inputs may cause stamping defects even with deep drawing materials. Limit states may then appear in the form of cracks or unacceptable thinning in the critically stressed areas of the stamped parts. For this reason, a general focus is placed on the use of non-destructive methods and inspection of stamped parts after stamping for potential subsequent modification of the stamping process. The presented work deals with the material analyses of stamped parts made of Bake-Hardened Interstitial-Free steel, including the local thickness reduction of the material, leading to the occurrence of crack propagation. The focus of the work was placed on the critical influencing factors resulting from the limit states presented. The evaluation of the material flow and the local plastic response was carried out using a cylindrical indentation method. In addition, the SEM analyses showed the importance of the deformation capacity of the surface coating which proved to be one of the decisive parameters for the occurrence of limit states.

Indentation behavior of a semi-infinite piezoelectric semiconductor under a rigid flat-ended cylindrical indenter

Indentation behavior of a semi-infinite piezoelectric semiconductor under a rigid flat-ended cylindrical indenter

Towards understanding the influence of structured indenters geometry on material deformation behavior of indentation process

Nanoindentation has emerged as a pioneering technique for fabricating array structures at the nanoscale. This research incorporates molecular dynamics simulations to investigate the deformation mechanisms of materials influenced by structured indenters exhibiting diverse geometries. The primary objective of this study is to mitigate interference during the continuous indentation applied by the indenters, diminish the material's elastic recovery, and minimize the occurrence of defects. The simulation results unveil that plastic deformation of the workpiece induced by structured indenters manifests through the nucleation and slip of dislocations. The cylindrical indenter engenders the most pronounced residual indentation morphology, accompanied by substantial pile-up interference and an extensive range of dislocation expansion, surpassing that of other indenters. Conversely, pyramidal indenters exhibit minimal residual indentation morphology, albeit displaying considerable elastic recovery. A comprehensive evaluation that considers factors such as recovery after indentation, ease of processing, system stability, and material transfer against the indentation force is imperative for the determination of the ideally structured indenter. The meticulous analysis supports the efficacy of paraboloidal indenters possessing smaller taper angles in attaining consistent processing results, rendering them highly suitable for continuous indentation processing. The research content bears significant implications for advancing the application of structured indenters.

Mechanical properties and deformation mechanisms of two-dimensional borophene under different loadings

Two-dimensional (2D) borophene has attracted widespread research interest in condensed matter physics and materials science because of its rich physical and chemical properties. However, the mechanical properties and deformation mechanisms of borophene under different loadings are still unclear and not thoroughly investigated. In this work, the tensile, shear, and nanoindentation failure processes of borophene are simulated via molecular dynamics method to obtain the key mechanical parameters of borophene. The mechanical response and deformation mechanism of borophene under different loads are analyzed from the change of B—B bond length with the strain/indentation depth. The results show that the tensile mechanical properties of borophene exhibit significant anisotropic characteristics, with the Young’s modulus and strength along the armchair direction being much higher than those along the zigzag direction. However, the anisotropy of the shear mechanical properties of borophene is not significant. This phenomenon can be attributed to the different contributions of the strong B—B σ bonds and weak multi-center bonds in borophene when they are stretched in different directions. It is also found that borophene exhibits different mechanical responses under spherical indentation and cylindrical indentation. The force at failure of the borophene under spherical indentation is much lower than the value under cylindrical one, and the intrinsic mechanical parameters of borophene under spherical indentation cannot be estimated accurately because of the anisotropic characteristics of borophene. However, under cylindrical indentation, borophene exhibits similar anisotropic characteristics to those under tension, and the mechanical parameters such as Young’s modulus can be measured accurately, which are consistent with those obtained under tension. In addition, the effects of the borophene indentation model and spherical/cylindrical indenter size, the loading rate and temperature on the mechanical parameters of borophene are also studied systematically. The results indicate that the Young’s modulus of borophene from spherical indentation is highly estimated when <i>a</i>/<i>R</i> < 15 but not sensitive when <i>a</i>/<i>R</i> > 15, while the results from cylindrical indentation are hardly affected by the values of <i>L</i>/<i>R</i> and <i>W</i>/<i>L</i>. The Young’s modulus of borophene slightly decreases with temperature increasing, while the loading rate has almost no influence on the value of Young’s modulus of borophene. These findings are expected to provide important guidelines for realizing the practical applications of borophene based micro/nano electromechanical systems.

Contact behaviors involving a nanobeam with surface effect by a rigid indenter

In this study, we present a novel surface model that utilizes surface energy density to predict the surface effect in nanobeam contact problems. To address the issue of a finite-length elastic nanobeam being indented by a rigid cylindrical indenter, we propose an equivalent substitution method. This method allows us to formulate analytical relations between the load and contact half-width for two different boundary cases. The explicit expressions of the contact-zone width, the pressure distribution in the contact zone, the deflection outside the contact zone, and the load–displacement relation are obtained for the nanobeam with surface effect and are compared with classical results in detail. The results show that the influence of the surface effect is very significant for nanobeam contact behavior, especially when the half-width of the contact zone increases and the contact zone becomes two independent symmetric strips. It is also found that the length-height ratio of nanobeam and the end support conditions have a fairly obvious effect on the normalized pressure distribution, which deviates significantly from the one predicted by the classical results due to the surface effect. However, for a given beam length and indenter radius, the ratio of the width of the contact zone to the beam thickness is almost constant, independent of the indenter load and beam boundary conditions. Meanwhile, the model predicts that the contact pressure distribution after the normalization of the average indentation pressure is almost independent of the indentation load and beam boundary conditions, but obviously depends on the surface effect parameters. The present method and result should be helpful not only to the measurement of mechanical properties of the indentation nanobeam but also to the design of the nanobeam-based devices.

Surface Effect in Nano-Scale Fretting Contact Problems

Abstract The fretting contact behavior of nanostructured materials is significantly influenced by the surface effect. A model of fretting contact between a nano-sized rigid cylindrical indenter and an elastic half-plane is established based on Gurtin–Murdoch (G–M) surface elasticity theory, with which the surface effects on the stress and displacement distributions and the size of stick region (no-slip region) in the contact zone are systematically studied. It is found that the surface effect induces an additional traction besides the external force applied by punch, which could help to smoothen the stress and displacement distributions. The normal surface-induced traction related to the residual surface stress is opposite to the externally applied compression, which results in a material stiffening in the contact zone so that the contact radius, normal displacement, and normal stress decrease compared with their classical counterparts. The tangential surface-induced traction is also opposite to the externally applied frictional stress, consequently leading to reductions of the shear stress and tangential displacement induced by friction in the contact zone. More interestingly, the surface effect leads to three possible states in the contact zone, including complete slip, partial slip, and complete stick, instead of the solely partial slip state in classical fretting contact models without surface effect. Among them, the complete stick due to the action of surface residual stress is more beneficial for inhibiting the wear of contact devices, which can be realized by reducing the indenter size. The present research does not only help one to better understand the physical mechanism in nano-scale fretting contact problems, but should also guide the anti-wear design in nano-electro-mechanical (NEMs) systems.

Novel procedure to determine the stress-strain relation of Lithium-ion Batteries through indentation test

This study proposes a novel approach to convert the load–depth curve measured in the experimental indentation test into stress–strain curves. Due to the lack of the tensile test results for the cylindrical lithium-ion battery (LIB) cell, a combination of the analytical analysis and the inverse optimization approach is first conducted as a reference point to determine the elastoplastic constitutive equation, which can predict the response of cylindrical LIB cell cells under the cylindrical indenter. The obtained load-depth curves from the robust optimization algorithm are in good agreement with the experimental loading–unloading curves. This novel approach includes a new definition of the contact area between the cylindrical indenter and the cylindrical LIB cell. Finite element models validate the measured contact area values from the analytical approach. The analytical approach in this study can accurately capture the stress–strain curve validated with optimization results. Afterward, different single indentation tests are conducted to estimate the reduction of Young’s modulus through the increasing indentation depth. Noteworthy, a definition of the indentation strain can physically interpret the indentation strain in the case of two crossed cylinders. The cell voltage is measured during the indentation test to detect the internal short circuit in the LIB cell. In homogenized modeling, the damage of the LIB cell is considered, which is an essential indicator of the internal short circuit of a LIB cell and possible thermal runaway.

Semi-analytical creep model to obtain Norton's law of materials under flat indentation and its applications

In traditional indentation test methods for obtaining Norton's law of creep materials, an empirical correlation formula represents the relationship between the indentation strain rate and the uniaxial reference strain rate or indentation displacement rate. This study proposes an equivalent method for representative volume elements (RVE) of creep materials from a complex stress state to a simple stress state. Considering Norton's law as a constitutive relationship based on the equivalent method of stress state, a semi-analytical model describing the creep displacement vs. time relationship of flat cylindrical indentation (flat indentation) and a method for determining the parameters of the model were established under constant load conditions in this investigation. The finite element analysis (FEA), creep test results of zinc alloy ZA27, and results in the current literature were used to verify the semi-analytical creep model. The results showed that Norton's law and the displacement rate predicted by different indentation creep models are relatively close, and the partial results predicted by the new model are slightly better than those obtained by methods reported in the literature.

Origami-inspired sandwich structures under low-to-high velocity impacts: A numerical simulation approach

In this study, the ballistic impact performance of sandwich structures with Miura-origami pattern inspired core (MPIC) panels subjected to low-to-high velocity impacts is studied. Sandwich panels with MPIC structure were modeled and finite element analysis was performed using commercially available software LS-DYNA to evaluate their specific energy absorption (SEA) and load-bearing capabilities. A cylindrical indenter (diameter = 10 mm and height = 15 mm) with material property of mild Steel (ρ = 7800 kg/m3) was impacted at three different velocities, i.e., 10 m/s (0.46 J), 50 m/s (11.49 J), 100 m/s (45.95 J) under predefined impact conditions. The obtained results were compared with that of a monolithic solid plate under identical loading conditions and geometrical dimensions. The proposed MPIC design was 93% lighter in weight than the monolithic solid plate. On comparison of stress contours, the monolithic solid plate exhibited regions of high-stress concentration at the impact zone. However, for the MPIC sandwich panel, the stress contour was found to be uniform. For an impact velocity of 100 m/s, the SEA of the MPIC sandwich panel was found to be 1142.6 J/kg, while for the monolithic solid plate, it was obtained as 57.17 J/kg. Eventhough complete penetration of the MPIC sandwich panel occurred for an impact velocity of 100 m/s, the SEA of the MPIC sandwich panels were found to be significantly higher than that of the monolithic solid plate. Since MPIC sandwich panels exhibit enhanced energy dissipation characteristics, they can be an alternative to the conventional monolithic solid plate as light-weight high performance designs for specific applications.